Convex Analysis

Adil Bagirov (), Napsu Karmitsa () and Marko M. Mäkelä ()
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Adil Bagirov: School of Information Technology and Mathematical Sciences, University of Ballarat
Napsu Karmitsa: University of Turku
Marko M. Mäkelä: University of Turku

Chapter Chapter 2 in Introduction to Nonsmooth Optimization, 2014, pp 11-60 from Springer

Abstract: Abstract The theory of nonsmooth analysis is based on convex analysis. Thus, we start this chapter by giving basic concepts and results of convexity. We take a geometrical viewpoint by examining the tangent and normal cones of convex sets. Then we generalize the concepts of differential calculus for convex, not necessarily differentiable functions. We define subgradients and subdifferentials and present some basic results. At the end of this chapter, we link these analytical and geometrical concepts together.

Keywords: Normal Cone; Subdifferential; Subgradient; Contingent Cone; Supporting Hyperplanes (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-08114-4_2

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DOI: 10.1007/978-3-319-08114-4_2

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